Initial Layer Problem of the Electro-diffusion Model Arising in Electrohydrodynamics

The authors study the electro-diffusion model arising in electrohydrodynamics which is a coupled Poisson-Nernst-Planck and Navier-Stokes system. On the basis of the general data,a more accurate approximate solution involving the effect of initial layer is constructed and the quasi-neutral limit is performed rigorously by using multiple scaling asymptotic analysis. Hardy-Littlewood's inequality is used to deal with the singular terms caused by the initial layer function.